Unfortunately the early Catholic registers give very little detail to work with, no residence occupations or father's names etc. - so difficult to be certain of any possible lines working back. The entry in the marriage register (see towards the bottom of the right hand page) only includes the date, names of the couple and the names of the witnesses, neither with the same surnames as the couple. Marriages generally took place in the bride's parish so it's possible that's the parish Many Ann was baptised in, but with such a common surname and no additonal clues it would be difficult to be certain of an possible baptism matches.
A general search for possible baptisms for Edward or equivilent Edmond in the Dublin city records on the free IrishGenealogy website show quite a number of potential matches - approx. 10, the difficulty is figuring out if 'your' Edward is one of these or possibly moved to the city and was born somewhere outside Dublin city (Note - the IrishGenealogy website does not include at least one major Catholic parish in DUblin city - St Pauls, Arran Quay).
Did your Edward and Mary-Anne stay in Ireland ? I had a quick search for possible baptisms of children but didn't locate any promising matches in Dublin.